This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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Here are the solutions for the fraction problems:
a) Step 1: Add the numerators. Step 2: Convert the improper fraction to a mixed number. The answer is \boxed{1\frac{1{5}}}.
b) Step 1: Add the numerators. Step 2: Convert the improper fraction to a mixed number. The answer is \boxed{1\frac{2{9}}}.
c) Step 1: Subtract the numerators. The answer is \boxed{\frac{1{4}}}.
d) Step 1: Add the numerators. Step 2: Convert the improper fraction to a mixed number. Step 3: Simplify the fraction part. The answer is \boxed{1\frac{1{5}}}.
e) Step 1: Add the numerators. Step 2: Convert the improper fraction to a mixed number. Step 3: Simplify the fraction part. The answer is \boxed{1\frac{1{3}}}.
f) Step 1: Add the numerators. Step 2: Convert the improper fraction to a mixed number. The answer is \boxed{1\frac{4{7}}}.
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a) Step 1: Add the numerators. (2)/(5) + (4)/(5) = (2+4)/(5) = (6)/(5) Step 2: Convert the improper fraction to a mixed number.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.